Hi Jennifer, interesting debacle. I think my first opinion would be to an awning, maybe even retractable awning like a sunsetter type to go under the bay window.
I’m not sure if you were thinking of something more solid than that although it doesn’t look like there’s much room as it really needs to be attached somewhere around the sides and front of the bay window. As far as the bump out next to it I wouldn’t suggest any awning/patio cover over that section as the windows won’t match up with the proper alignment. What do you think? :-) Darren